Algebra B.Sc. 3rd Sem. Mathmatics Testbook Ramprasad

       Algebra Part-A is a crucial textbook for B.Sc. 2nd Year 3rd Semester students, authored by distinguished scholars Dr. R.C. Singh Chandel, Dr. Vidya Sagar Chaubey, Dr. Vijai Shankar Verma, and Dr. Prateek Mishra. Published by Ram Prasad Pub. Agra, this 344-page book provides a comprehensive study of algebraic concepts, essential for a deep understanding of higher mathematics.

Authors’ Background:

• Dr. R.C. Singh Chandel (D.V. (P.G.) College, Orai, Jalaun)
• Dr. Vidya Sagar Chaubey (B.R.D. (P.G.) College, Deoria)
• Dr. Vijai Shankar Verma (D.D.U. Gorakhpur)
• Dr. Prateek Mishra (M.L.K. (P.G.) College, Balrampur)

Contents Overview:

Unit I:

1. Introduction to Indian Ancient Mathematics and Mathematicians (Pages 1-24)
   • Overview of ancient Indian contributions to mathematics.
   • Key mathematicians and their works.
2. Equivalence Relations and Partitions, Congruence Modulo (Pages 25-64)
   • Fundamental concepts of equivalence relations and partitions.
   • Detailed study of congruence modulo.
3. Group Theory (Pages 65-126)
   • Introduction to group theory and its basic properties.
   • In-depth exploration of groups and their structures.
4. Sub-groups (Pages 127-142)
   • Detailed study of sub-groups and their characteristics.
5. Cyclic Groups (Pages 143-156)
   • Analysis of cyclic groups and their properties.

Unit II: 6. Permutation Groups (Pages 157-193)

• Comprehensive study of permutation groups and their applications.

7. Cosets and Cosets Decomposition (Pages 194-215)
   • Detailed exploration of cosets and their decompositions.

Unit III: 8. Normal Subgroups (Pages 216-228)

• In-depth study of normal subgroups and their significance.

9. Quotient Groups (Pages 229-234)
   • Detailed analysis of quotient groups and their properties.
10. Homomorphism and Isomorphism of Groups (Pages 235-261)
    • Study of group homomorphisms and isomorphisms.

Unit IV: 11. Rings (Pages 262-284) – Introduction to ring theory and its applications.

12. Integral Domain (Pages 285-293)
    • Comprehensive study of integral domains and their properties.
13. Field (Pages 294-306)
    • Detailed exploration of fields and their structures.
14. Ideal and Quotient Rings, Ring Homomorphism, Field of Quotient of an Integral Domain (Pages 307-343)
    • In-depth study of ideals, quotient rings, ring homomorphisms, and the field of quotients of an integral domain.

Purpose and Audience:

Algebra Part-A not only prepares students for their academic exams but also lays a solid foundation for future studies and research in algebra and related fields. The book’s rigorous approach and thorough coverage make it an indispensable resource for both students and educators in higher mathematics.